How do you deal with more than one probable trading candidates for next day? Assumptions: You have a tested trading system. Your probable trading candidates all meet your trading system conditions.
I assume you mean you have too many candidates for your available capital. This is a large field of study - I can't really do this justice in a few sentences. You should run some monte carlo tests against a random selection of entries - make sure your system is robust enough to handle an alternative sequence of trades. If you have a trading system that generates more signals than available capital with a large universe then you could conisder a smaller universe (but of course, you need to backtest it). For example, if you are using Russell 3000 as your candidate list, you could try Russell 1000 instead, or S&P 500. Make sure you do not introduce survivorship bias. Alternatively, investigate ranking mechanisms (i.e. a signal score) and also backtest that. Ensure that such ranking is not forward looking. There's a few items for thought for you, but developing a robust system requires a lot more coverage than just these points.
You can tighten your conditions or add criteria. Personally when faced with that situation I rank them by risk/reward and after that i'll look at the charts and take the smoothest looking one.
KISS. Don't overfit. If your system generates a satisfactory result then choose the maximum of the number of stocks you are willing to trade Then choose those stocks at random.